Problem: Simplify to lowest terms. $\dfrac{70}{98}$
Explanation: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 70 and 98? $70 = 2\cdot5\cdot7$ $98 = 2\cdot7\cdot7$ $\mbox{GCD}(70, 98) = 2\cdot7 = 14$ $\dfrac{70}{98} = \dfrac{5 \cdot 14}{ 7\cdot 14}$ $\hphantom{\dfrac{70}{98}} = \dfrac{5}{7} \cdot \dfrac{14}{14}$ $\hphantom{\dfrac{70}{98}} = \dfrac{5}{7} \cdot 1$ $\hphantom{\dfrac{70}{98}} = \dfrac{5}{7}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{70}{98}= \dfrac{2\cdot35}{2\cdot49}= \dfrac{2\cdot 7\cdot5}{2\cdot 7\cdot7}= \dfrac{5}{7}$